The present invention relates to drafting instruments. More particularly, the present invention concerns a template for preparing axonometric drawings.
So-called xe2x80x9cmechanical drawingsxe2x80x9d are generally rendered using one of four different projections. In multi-view projection, the object is presented to the viewer on the drawing paper in front, side and top views. This method of projection is best for depicting objects of considerable complexity, and is ideal for showing dimensions, hidden lines, etc. However, a multi-view drawing is often difficult for persons not skilled in the drafting arts to visualize in three dimensions.
For this purpose, one of three xe2x80x9cpictorialxe2x80x9d projections is often used: oblique projection, perspective projection, and axonometric projection. In oblique projection, the observer is considered to be at an infinite distance from the object, hence lines between points on the object in real space and corresponding points on the rendered object on the plane of projection (i.e. the drawing sheet) are parallel, but form oblique angles with respect to the projection plane.
In perspective projection, typically used in art, the observer is considered to be at a finite distance from the projected object, and visual rays drawn from the observer""s eye (the xe2x80x9cstation pointxe2x80x9d) to all points of the object form a cone of rays. All lines which are parallel in the object in real space are thus seen as lines which converge to a xe2x80x9cvanishing pointxe2x80x9d on the horizon. This example of projection renders a three-dimensional object in a most visually xe2x80x9ccorrectxe2x80x9d manner on a two-dimensional surface, since this is the manner in which the human eye perceives objects in real space. Perspective projection is best illustrated in architectural paintings of the Renaissance Italianate school of painting. However, since parallel lines on the real object converge to the vanishing point in the drawing, it is not possible to take dimensional measurements directly from the drawing.
Axonometric projections, as the name implies, permit measurements to be taken parallel to the coordinate axes of the drawing and are thus in common use in mechanical drafting. In axonometric projection, the object is inclined with respect to the plane of projection about two of its three Cartesian coordinate axes in real space with all imaginary lines drawn from points on the real object to corresponding points on the projected object being parallel. The general term xe2x80x9caxonometric projectionxe2x80x9d thus applies to the infinite variety of angles with which an object may be tilted or inclined with respect to the projection plane. These include so-called isometric, dimetric, and trimetric projections. Examples of these three types of axonometric projections are depicted in FIG. 1. In FIG. 1a, the front face 1-2-3-4 of a cube is shown in a typical multi-view drawing. FIG. 1b shows a trimetric projection of that cube; FIG. 1c depicts a dimetric projection; and FIG. 1d shows an isometric projection of the cube.
Rotation about the Cartesian coordinate axes of a real space object and subsequent projection upon a flat plane to produce an axonometric projection drawing results in the corresponding foreshortening of the scales of the axes. In an isometric projection, the rotation is about two of the three axes by equal amounts of 45xc2x0. The result is that the scales of all three coordinate axes in the projected drawing are foreshortened by the same amount. In a dimetric projection, rotation of the Cartesian coordinate axes similarly takes place around two of the axes, but rotation about one of the axes is through an angle of 45xc2x0, while rotation about the other axis is through an acute angle other than 45xc2x0. There results a similar foreshortening of the scales of the three axes, but with two of the axial scales foreshortened by the same amount, and the third by a different amount. Finally, in a trimetric projection, rotation of the Cartesian coordinate axes takes place about two of the three axes, but through unequal acute angles not equal to 45xc2x0. In this case, the scales of all three rotated coordinate axes are foreshortened, but by unequal amounts.
Typically, axonometric drawings are prepared either manually, with the aid of a T-square and a drawing triangle having the appropriate angles, by a mechanical drafting machine, or more recently, by a computer-assisted design (CAD) software program and computer. However, there are numerous occasions where axonometric drawings or sketches must be prepared under circumstances where neither the necessary drafting instruments or a properly programmed computer is available. In these situations, there is a need for a drafting device which is inexpensive, easily transportable, and simple to use, but which renders axonometric drawings of a quality equal to those rendered by a drafting machine or by CAD.
The present invention provides, in its principal embodiment, drafting template for preparing axonometric drawings or sketches comprising a unitary, clear, substantially planar, chevron-shaped body having an apex and an antapex, an upper face, a lower face, and at least six side edges.
The unitary chevron-shaped drafting template of the present invention, if divided into two legs by a line connecting the apex and antapex, in various embodiments describes a shape in which either or both legs may be the shape of a trapezoid or parallelogram and may be of equal or different lengths.
Depending upon the angles formed between a first upper edge of the drafting template and the line connecting the apex and antapex, and between the second upper edge of the drafting template and the line connecting the apex and antapex, the drafting template of the present invention in various embodiments is adapted for rendering trimetric, dimetric or isometric drawings.
In a preferred embodiment, the drafting template of the present invention further comprises indicia disposed on a face of the body for measuring and scaling the drawing or sketch.